#5;
#psolution1(c_,d_,y_,x_,n_):=if(isfree(c,d,y), if(isfree(c,d,x), -d/c, if(n==2, if(isfree(c,x), 
	if(c<0, expand((cos(sqrt(-c)*x)*int(d*sin(sqrt(-c)*x),x)-sin(sqrt(-c)*x)*int(d*cos(sqrt(-c)*x),x))/2/sqrt(-c)),
		expand((exp(sqrt(c)*x)*int(d*exp(-sqrt(c)*x),x)-exp(-sqrt(c)*x)*int(d*exp(sqrt(c)*x),x))/2/sqrt(c)) )),
	if(isinteger(n), block(dsolve:=integrate(c,x), expand(exp(dsolve)*integrate(d*exp(-dsolve),x))),
	 int((x-z)^(n-1)*replace(d,x,z)*mittag(n,n,replace(int(c,x,n),x,x-z)*n!), z,0,x) ))));
#psolution1(c_,d_,y_,x_,n_):=if(isfree(c,d,y) and n<1, block(gs:=gsolution(c,y,x,n)/C_1, int(simplify(d/gs),x,n)*gsolution(c,y,x,n)/C_1) );
#psolution1(c_,d_,y_,x_,n_):=if(isfree(c,d,y) and n<=1, block(gs:=gsolution(c,y,x,n)/C_1, int(simplify(d/gs),x,n)*gs) );
#psolution(c_,d_,y_,x_,2):=if(isfree(c,d,y) and isfree(c,x),if(c<0, cos(sqrt(-c)*x)*int(d*sin(sqrt(-c)*x),x)/2/sqrt(-c)-sin(sqrt(-c)*x)*int(d*cos(sqrt(-c)*x),x)/2/sqrt(-c),
	expand(exp(sqrt(c)*x)*int(d*exp(-sqrt(c)*x),x)/2/sqrt(c)-exp(-sqrt(c)*x)*int(d*exp(sqrt(c)*x),x)/2/sqrt(c)) ));

psolution1(c_,d_,y_,x_,n_):=if(isfree(d/c,x), -d/c, 
	if(n>0 and n<=1, if(c>0, expand(integrate(d*exp(-c^(1/n)*x),x,n)*exp(c^(1/n)*x)),
	block(dsolve:=n!*integrate(c,x,n), expand(integrate(d/mittag(n,dsolve),x,n)*mittag(n,dsolve))) 
	)));

#psolution1(b_,x_^n_, y_,x_,q_) := If(isfree(b,x) and isfree(b,y) and n>0, if(q==n,-x^n/b-n!, 
	if(q-n>0,-x^n/b, 
	if(isinteger(n) or isinteger(n-q),-sum(b^(-1-k/q)*n!/(n-k)!*x^(n-k),k,0,n,q),
	-gamma(n+1,b*x)*exp(b*x) ))));


psolution1(c_,g_,y_,x_,-1):=if(hasnot(g/c,x),-g/c, if(hasnot(c,g,E(0.5,x)) and hasnot(c,x), block(f:= -psolution(1/c,d(g,x)/c,y,x,1),
	if(hasnot(f,int(y(x),x)),f) )));
#psolution(c_,g_,y_,x_,-0.5):=if(hasnot(g/c,x),-g/c, if(hasnot(c,g,E(0.5,x)) and hasnot(c,x) and hasnot(g,f(x)), block(f:= -psolution(1/c^2,d(g,x)/c+d(g,x,0.5)/c^2,y,x,1),
	if(hasnot(f,int(y(x),x)),f) )));
#psolution(c_,g_,y_,x_,0.5):=if(hasnot(g/c,x),-g/c, if(hasnot(c,g,E(0.5,x)) and hasnot(c,x) and hasnot(g,f(x)), block(f:=psolution(c*c,d(g,x,0.5)+c*g,y,x,1),
	if(hasnot(f,int(y(x),x)),f) )));
#psolution1(c_,g_,y_,x_,1/2):=if(hasnot(g/c,x),-g/c, if(hasnot(c,g,E(0.5,x)), psolution(c*c+d(c,x,0.5),d(g,x,0.5)+c*g,y,x,1) ));
psolution1(c_,d_,y_,x_,4):=if(isfree(c,x), gsolution1(c,y,x,4)*int(d*gsolution2(c,y,x,4),x)/(4*(c)^(3/4))
	-gsolution2(c,y,x,4)*int(d*gsolution1(c,y,x,4),x)/(4*(c)^(3/4))+gsolution3(c,y,x,4)*int(d*gsolution4(c,y,x,4),x)/(2*(c)^(3/4))
	-gsolution4(c,y,x,4)*int(d*gsolution3(c,y,x,4),x)/(2*(c)^(3/4))  );
psolution1(c_,d_,y_,x_,3):=if(isfree(c,x), (gsolution1(c,y,x,3)*int(d*gsolution2(c,y,x,3),x)+gsolution2(c,y,x,3)*int(d*gsolution3(c,y,x,3),x)
	+gsolution3(c,y,x,3)*int(d*gsolution1(c,y,x,3),x))/(3cbrt(3)*c^(2/3)) );
psolution1(c_,d_,y_,x_,2):=if(isfree(c,x),if(isfree(d,x), -d/c,  
	if(c<0, expand((cos(sqrt(-c)*x)*int(d*sin(sqrt(-c)*x),x)-sin(sqrt(-c)*x)*int(d*cos(sqrt(-c)*x),x))/sqrt(-c)),
	expand((exp(sqrt(c)*x)*int(d*exp(-sqrt(c)*x),x)-exp(-sqrt(c)*x)*int(d*exp(sqrt(c)*x),x))/2/sqrt(c)) )));

psolution1(c_,g_,y_,x_,1):=if(hasnot(g/c,x),-g/c, if(isfree(c,g,y), 
	block(f:=integrate(c,x), exp(f)*integrate(exp(-f)*g,x)) ));

#7;
psolution1(b_,m_,c_,d_,y_,x_,n_):= if(hasnot(d,y),if(c==0,-int(d,x,m),
	if(hasnot(d/c,x),  if(m==1,-d/c*x, -d/c),
	if(hasnot(b/c,x) and hasnot(d/c/x,x),if(m==1, b/c^2*d/x-d/c, -d/c),
	if(b+c*x<>0 and hasnot(d/(b+c*x),x),-d*x/(b+c*x) 
	)))));
psolution1(b_,1,c_,d_,y_,x_,2):= if(c==0,-int(d,x),
	if(hasnot(d/c,x),  -d/c, 
	if(hasnot(b/c,x) and hasnot(d/c/x,x),  b/c^2*d/x-d/c, 
	if(b+c*x<>0 and hasnot(d/(b+c*x),x), -d*x/(b+c*x), 
	if(hasnot(b,c,y) and hasnot(b,c,x), 
	if(b*b+4c==0,  (exp(b/2*x)*x*int(exp(-b/2*x)*d,x)-exp(b/2*x)*int(d*exp(-b/2*x)*x,x)),
	((-exp((b-sqrt(b^2+4c))/2*x)*int(d*exp((-b+sqrt(b^2+4c))/2*x),x)+exp((b+sqrt(b^2+4c))/2*x)*int(d*exp((-b-sqrt(b^2+4c))/2*x),x))/sqrt(b*b+4c)) 
	))))));

psolution1(b_,m_,c_,c1_*c2_,y_,t_,n_):=if(hasnot(c1,t) and hasnot(c1,x), c1*psolution(b,m,c,c2,y,t,n), if(hasnot(c2,t) and hasnot(c2,x), c2*psolution(b,m,c,c1,y,t,n),
	if(m==1 and n==1 and has(c1,t) and hasnot(c1,x), if(c==0, int(replace(c1,t,t-x/b+z/b)*replace(c2,x,z),z,1,x)/b,
	int(exp(-c*z/b)*replace(c1,t,t-x/b+z/b)*replace(c2,x,z),z,1,x)*exp(c*x/b)/b ))));
psolution1(f_,p_,0,g_,y_,x_,q_):= int(psolution(f,g,y,x,q-p),x,p);


#8;
psolution1(b_,m_,c_,d_,y_,t_,x_,p_):= if(isconstant(d),if(c==0,-d*t^p/p!, -d/c),
	if(hasnot(c,d,x), psolution(-c,-d,y,t,p),
	if(hasnot(c,d,t), if(hasnot(b,t),psolution(-c/b,-d/b,y,x,m), psolution(-c,-d,y,x,m)
	))));
#psolution1(b_,1,0,d_,y_,t_,x_,1):= if(has(d,t) and has(d,x), -int(replace(replace(d,t,z),x,x-b*t+b*z),z,0,t) );
psolution1(b_,m_,0,d_,y_,t_,x_,p_):= 
	if(has(d,t) and has(d,x), if(isfunction(d), -d(argument(d,1),t)^m*int(d,t,p)/(d(argument(d,1),t)^m+b*d(argument(d,1),x)^m) ),
	if(hasnot(d,x), -int(d,t,p),
	if(has(d,x), if(hasnot(b,d,t), -int(d/b,x,m), -int(d,x,m)),
	-int(replace(replace(d,t,z),x,x-b*t+b*z),z,0,t) )));

psolution1(b_,m_,c_,c1_*c2_,y_,t_,x_,p_):=if(isconstant(c1), c1*psolution1(b,m,c,c2,y,t,x,p), if(isconstant(c2), c2*psolution1(b,m,c,c1,y,t,x,p) ));
psolution1(b_,m_,c_,c1_+c2_,y_,t_,x_,n_):= psolution1(b,m,c,c1,y,t,x,n)+psolution1(b,m,c,c2,y,t,x,n);


#9;
psolution1(a_,n_,b_,m_,c_,d_,y_,x_,p_):= if(isconstant(p),if(c<>0 and isconstant(d),-d/c, if(has(d,t), psolution1(b,m,c,d,y,t,p), if(has(d,x), psolution1(b/a,m,c/a,d/a,y,x,n) ))),
	if(hasnot(a,c,d,x), psolution1(-c/a,-d/a,y,t,n), if(hasnot(b,c,d,t), psolution1(-c/b,-d/b,y,x,m) )));

psolution1(a_,n_,b_,m_,c_,c1_*c2_,y_,t_,p_):= if(isconstant(c1), c1*psolution1(a,n,b,m,c,c2,y,t,p), if(isconstant(c2), c2*psolution1(a,n,b,m,c,c1,y,t,p) ));
psolution1(a_,n_,b_,m_,c_,c1_*c2_*c3_,y_,t_,p_):= if(isconstant(c1), c1*psolution1(a,n,b,m,c,c2*c3,y,t,p), if(isconstant(c2), c2*psolution1(a,n,b,m,c,c1*c3,y,t,p) ));

psolution1(a_,n_,b_,m_,c_,c1_+c2_,y_,x_,p_):=psolution1(a,n,b,m,c,c1,y,x,p)+psolution1(a,n,b,m,c,c2,y,x,p);